LMFDB - Embedded newform 245.4.e.i.116.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(116,245)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("245.116");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.4.e.i.226.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.70711 - 4.68885i) q^{2} +(-2.32843 + 4.03295i) q^{3} +(-10.6569 + 18.4582i) q^{4} +(-2.50000 - 4.33013i) q^{5} +25.2132 q^{6} +72.0833 q^{8} +(2.65685 + 4.60181i) q^{9} +O(q^{10})$	\(q+(-2.70711 - 4.68885i) q^{2} +(-2.32843 + 4.03295i) q^{3} +(-10.6569 + 18.4582i) q^{4} +(-2.50000 - 4.33013i) q^{5} +25.2132 q^{6} +72.0833 q^{8} +(2.65685 + 4.60181i) q^{9} +(-13.5355 + 23.4442i) q^{10} +(26.1274 - 45.2540i) q^{11} +(-49.6274 - 85.9572i) q^{12} -30.6569 q^{13} +23.2843 q^{15} +(-109.882 - 190.322i) q^{16} +(18.6127 - 32.2381i) q^{17} +(14.3848 - 24.9152i) q^{18} +(40.1127 + 69.4772i) q^{19} +106.569 q^{20} -282.919 q^{22} +(-12.9167 - 22.3724i) q^{23} +(-167.841 + 290.708i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(82.9914 + 143.745i) q^{26} -150.480 q^{27} +20.9411 q^{29} +(-63.0330 - 109.176i) q^{30} +(-157.279 + 272.416i) q^{31} +(-306.593 + 531.035i) q^{32} +(121.672 + 210.741i) q^{33} -201.546 q^{34} -113.255 q^{36} +(-98.5736 - 170.734i) q^{37} +(217.179 - 376.165i) q^{38} +(71.3823 - 123.638i) q^{39} +(-180.208 - 312.130i) q^{40} -11.3625 q^{41} -33.8335 q^{43} +(556.872 + 964.531i) q^{44} +(13.2843 - 23.0090i) q^{45} +(-69.9340 + 121.129i) q^{46} +(-180.838 - 313.221i) q^{47} +1023.41 q^{48} +135.355 q^{50} +(86.6766 + 150.128i) q^{51} +(326.706 - 565.871i) q^{52} +(-76.5097 + 132.519i) q^{53} +(407.366 + 705.579i) q^{54} -261.274 q^{55} -373.598 q^{57} +(-56.6899 - 98.1897i) q^{58} +(-308.000 + 533.472i) q^{59} +(-248.137 + 429.786i) q^{60} +(7.63247 + 13.2198i) q^{61} +1703.09 q^{62} +1561.80 q^{64} +(76.6421 + 132.748i) q^{65} +(658.756 - 1141.00i) q^{66} +(83.2548 - 144.202i) q^{67} +(396.706 + 687.114i) q^{68} +120.303 q^{69} -952.000 q^{71} +(191.515 + 331.713i) q^{72} +(-74.2447 + 128.596i) q^{73} +(-533.698 + 924.393i) q^{74} +(-58.2107 - 100.824i) q^{75} -1709.90 q^{76} -772.958 q^{78} +(-428.862 - 742.812i) q^{79} +(-549.411 + 951.608i) q^{80} +(278.647 - 482.631i) q^{81} +(30.7595 + 53.2769i) q^{82} -660.528 q^{83} -186.127 q^{85} +(91.5908 + 158.640i) q^{86} +(-48.7599 + 84.4546i) q^{87} +(1883.35 - 3262.06i) q^{88} +(-22.8873 - 39.6420i) q^{89} -143.848 q^{90} +550.607 q^{92} +(-732.426 - 1268.60i) q^{93} +(-979.096 + 1695.84i) q^{94} +(200.563 - 347.386i) q^{95} +(-1427.76 - 2472.95i) q^{96} -1682.13 q^{97} +277.667 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} + 2 q^{3} - 20 q^{4} - 10 q^{5} + 16 q^{6} + 96 q^{8} - 12 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 + 2 * q^3 - 20 * q^4 - 10 * q^5 + 16 * q^6 + 96 * q^8 - 12 * q^9	\( 4 q - 8 q^{2} + 2 q^{3} - 20 q^{4} - 10 q^{5} + 16 q^{6} + 96 q^{8} - 12 q^{9} - 40 q^{10} + 14 q^{11} - 108 q^{12} - 100 q^{13} - 20 q^{15} - 168 q^{16} - 50 q^{17} - 16 q^{18} + 36 q^{19} + 200 q^{20} - 368 q^{22} - 244 q^{23} - 496 q^{24} - 50 q^{25} + 216 q^{26} - 172 q^{27} - 52 q^{29} - 40 q^{30} - 120 q^{31} - 672 q^{32} + 498 q^{33} + 48 q^{34} - 272 q^{36} - 564 q^{37} + 320 q^{38} + 14 q^{39} - 240 q^{40} + 656 q^{41} - 520 q^{43} + 1164 q^{44} - 60 q^{45} - 704 q^{46} - 350 q^{47} + 2736 q^{48} + 400 q^{50} + 754 q^{51} + 628 q^{52} + 56 q^{53} + 648 q^{54} - 140 q^{55} - 1336 q^{57} + 8 q^{58} - 1232 q^{59} - 540 q^{60} + 336 q^{61} + 2400 q^{62} + 4256 q^{64} + 250 q^{65} + 1976 q^{66} + 152 q^{67} + 908 q^{68} - 2664 q^{69} - 3808 q^{71} + 800 q^{72} + 676 q^{73} - 2016 q^{74} + 50 q^{75} - 3536 q^{76} - 880 q^{78} - 1014 q^{79} - 840 q^{80} + 1454 q^{81} - 816 q^{82} + 752 q^{83} + 500 q^{85} + 768 q^{86} - 410 q^{87} + 4688 q^{88} - 216 q^{89} + 160 q^{90} + 528 q^{92} - 2760 q^{93} - 1928 q^{94} + 180 q^{95} - 2464 q^{96} - 5484 q^{97} + 1880 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 2 * q^3 - 20 * q^4 - 10 * q^5 + 16 * q^6 + 96 * q^8 - 12 * q^9 - 40 * q^10 + 14 * q^11 - 108 * q^12 - 100 * q^13 - 20 * q^15 - 168 * q^16 - 50 * q^17 - 16 * q^18 + 36 * q^19 + 200 * q^20 - 368 * q^22 - 244 * q^23 - 496 * q^24 - 50 * q^25 + 216 * q^26 - 172 * q^27 - 52 * q^29 - 40 * q^30 - 120 * q^31 - 672 * q^32 + 498 * q^33 + 48 * q^34 - 272 * q^36 - 564 * q^37 + 320 * q^38 + 14 * q^39 - 240 * q^40 + 656 * q^41 - 520 * q^43 + 1164 * q^44 - 60 * q^45 - 704 * q^46 - 350 * q^47 + 2736 * q^48 + 400 * q^50 + 754 * q^51 + 628 * q^52 + 56 * q^53 + 648 * q^54 - 140 * q^55 - 1336 * q^57 + 8 * q^58 - 1232 * q^59 - 540 * q^60 + 336 * q^61 + 2400 * q^62 + 4256 * q^64 + 250 * q^65 + 1976 * q^66 + 152 * q^67 + 908 * q^68 - 2664 * q^69 - 3808 * q^71 + 800 * q^72 + 676 * q^73 - 2016 * q^74 + 50 * q^75 - 3536 * q^76 - 880 * q^78 - 1014 * q^79 - 840 * q^80 + 1454 * q^81 - 816 * q^82 + 752 * q^83 + 500 * q^85 + 768 * q^86 - 410 * q^87 + 4688 * q^88 - 216 * q^89 + 160 * q^90 + 528 * q^92 - 2760 * q^93 - 1928 * q^94 + 180 * q^95 - 2464 * q^96 - 5484 * q^97 + 1880 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.70711	−	4.68885i	−0.957107	−	1.65776i	−0.729472	−	0.684011i	$-0.760234\pi$
$2$	−2.70711	−	4.68885i	−0.957107	−	1.65776i	−0.227635	−	0.973746i	$-0.573099\pi$
$3$	−2.32843	+	4.03295i	−0.448106	+	0.776142i	−0.998263	−	0.0589190i	$-0.981235\pi$
$3$	−2.32843	+	4.03295i	−0.448106	+	0.776142i	0.550157	+	0.835061i	$0.314568\pi$
$4$	−10.6569	+	18.4582i	−1.33211	+	2.30728i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	25.2132			1.71554
$7$		0			0
$7$		0			0
$8$	72.0833			3.18566
$9$	2.65685	+	4.60181i	0.0984020	+	0.170437i
$10$	−13.5355	+	23.4442i	−0.428031	+	0.741372i
$11$	26.1274	−	45.2540i	0.716156	−	1.24042i	−0.246356	−	0.969179i	$-0.579233\pi$
$11$	26.1274	−	45.2540i	0.716156	−	1.24042i	0.962512	−	0.271239i	$-0.0874333\pi$
$12$	−49.6274	−	85.9572i	−1.19385	−	2.06781i
$13$	−30.6569			−0.654052			−0.327026	−	0.945015i	$-0.606047\pi$
$13$	−30.6569			−0.654052			−0.327026	+	0.945015i	$0.606047\pi$
$14$		0			0
$15$	23.2843			0.400798
$16$	−109.882	−	190.322i	−1.71691	−	2.97378i
$17$	18.6127	−	32.2381i	0.265544	−	0.459935i	−0.702162	−	0.712017i	$-0.747782\pi$
$17$	18.6127	−	32.2381i	0.265544	−	0.459935i	0.967706	+	0.252082i	$0.0811152\pi$
$18$	14.3848	−	24.9152i	0.188362	−	0.326253i
$19$	40.1127	+	69.4772i	0.484341	+	0.838904i	0.999838	−	0.0179877i	$-0.00572598\pi$
$19$	40.1127	+	69.4772i	0.484341	+	0.838904i	−0.515497	+	0.856891i	$0.672393\pi$
$20$	106.569			1.19147
$21$		0			0
$22$	−282.919			−2.74175
$23$	−12.9167	−	22.3724i	−0.117101	−	0.202825i	0.801517	−	0.597973i	$-0.204027\pi$
$23$	−12.9167	−	22.3724i	−0.117101	−	0.202825i	−0.918618	+	0.395147i	$0.870694\pi$
$24$	−167.841	+	290.708i	−1.42751	+	2.47253i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	82.9914	+	143.745i	0.625998	+	1.08426i
$27$	−150.480			−1.07259
$28$		0			0
$29$	20.9411			0.134092			0.0670460	−	0.997750i	$-0.478643\pi$
$29$	20.9411			0.134092			0.0670460	+	0.997750i	$0.478643\pi$
$30$	−63.0330	−	109.176i	−0.383607	−	0.664426i
$31$	−157.279	+	272.416i	−0.911232	+	1.57830i	−0.0989050	+	0.995097i	$0.531534\pi$
$31$	−157.279	+	272.416i	−0.911232	+	1.57830i	−0.812327	+	0.583203i	$0.801799\pi$
$32$	−306.593	+	531.035i	−1.69370	+	2.93358i
$33$	121.672	+	210.741i	0.641827	+	1.11168i
$34$	−201.546			−1.01661
$35$		0			0
$36$	−113.255			−0.524328
$37$	−98.5736	−	170.734i	−0.437984	−	0.758610i	0.559550	−	0.828797i	$-0.310974\pi$
$37$	−98.5736	−	170.734i	−0.437984	−	0.758610i	−0.997534	+	0.0701864i	$0.977641\pi$
$38$	217.179	−	376.165i	0.927133	−	1.60584i
$39$	71.3823	−	123.638i	0.293085	−	0.507638i
$40$	−180.208	−	312.130i	−0.712335	−	1.23380i
$41$	−11.3625			−0.0432810			−0.0216405	−	0.999766i	$-0.506889\pi$
$41$	−11.3625			−0.0432810			−0.0216405	+	0.999766i	$0.506889\pi$
$42$		0			0
$43$	−33.8335			−0.119990			−0.0599948	−	0.998199i	$-0.519108\pi$
$43$	−33.8335			−0.119990			−0.0599948	+	0.998199i	$0.519108\pi$
$44$	556.872	+	964.531i	1.90799	+	3.30474i
$45$	13.2843	−	23.0090i	0.0440067	−	0.0762219i
$46$	−69.9340	+	121.129i	−0.224157	+	0.388251i
$47$	−180.838	−	313.221i	−0.561233	−	0.972084i	−0.997389	−	0.0722130i	$-0.976994\pi$
$47$	−180.838	−	313.221i	−0.561233	−	0.972084i	0.436156	−	0.899871i	$-0.356339\pi$
$48$	1023.41			3.07743
$49$		0			0
$50$	135.355			0.382843
$51$	86.6766	+	150.128i	0.237983	+	0.412199i
$52$	326.706	−	565.871i	0.871268	−	1.50908i
$53$	−76.5097	+	132.519i	−0.198291	+	0.343450i	−0.947974	−	0.318347i	$-0.896872\pi$
$53$	−76.5097	+	132.519i	−0.198291	+	0.343450i	0.749684	+	0.661796i	$0.230206\pi$
$54$	407.366	+	705.579i	1.02658	+	1.77809i
$55$	−261.274			−0.640549
$56$		0			0
$57$	−373.598			−0.868145
$58$	−56.6899	−	98.1897i	−0.128340	−	0.222292i
$59$	−308.000	+	533.472i	−0.679630	+	1.17715i	0.295462	+	0.955354i	$0.404526\pi$
$59$	−308.000	+	533.472i	−0.679630	+	1.17715i	−0.975092	+	0.221800i	$0.928807\pi$
$60$	−248.137	+	429.786i	−0.533906	+	0.924752i
$61$	7.63247	+	13.2198i	0.0160203	+	0.0277479i	0.873924	−	0.486062i	$-0.161567\pi$
$61$	7.63247	+	13.2198i	0.0160203	+	0.0277479i	−0.857904	+	0.513810i	$0.828234\pi$
$62$	1703.09			3.48858
$63$		0			0
$64$	1561.80			3.05040
$65$	76.6421	+	132.748i	0.146251	+	0.253313i
$66$	658.756	−	1141.00i	1.22859	−	2.12799i
$67$	83.2548	−	144.202i	0.151809	−	0.262941i	−0.780084	−	0.625675i	$-0.784824\pi$
$67$	83.2548	−	144.202i	0.151809	−	0.262941i	0.931893	+	0.362735i	$0.118157\pi$
$68$	396.706	+	687.114i	0.707465	+	1.22537i
$69$	120.303			0.209895
$70$		0			0
$71$	−952.000			−1.59129			−0.795645	−	0.605763i	$-0.792868\pi$
$71$	−952.000			−1.59129			−0.795645	+	0.605763i	$0.792868\pi$
$72$	191.515	+	331.713i	0.313475	+	0.542955i
$73$	−74.2447	+	128.596i	−0.119037	+	0.206178i	−0.919386	−	0.393356i	$-0.871314\pi$
$73$	−74.2447	+	128.596i	−0.119037	+	0.206178i	0.800349	+	0.599534i	$0.204647\pi$
$74$	−533.698	+	924.393i	−0.838394	+	1.45214i
$75$	−58.2107	−	100.824i	−0.0896212	−	0.155228i
$76$	−1709.90			−2.58078
$77$		0			0
$78$	−772.958			−1.12205
$79$	−428.862	−	742.812i	−0.610770	−	1.05788i	−0.991111	−	0.133038i	$-0.957527\pi$
$79$	−428.862	−	742.812i	−0.610770	−	1.05788i	0.380341	−	0.924846i	$-0.375807\pi$
$80$	−549.411	+	951.608i	−0.767826	+	1.32991i
$81$	278.647	−	482.631i	0.382232	−	0.662045i
$82$	30.7595	+	53.2769i	0.0414246	+	0.0717494i
$83$	−660.528			−0.873523			−0.436761	−	0.899577i	$-0.643875\pi$
$83$	−660.528			−0.873523			−0.436761	+	0.899577i	$0.643875\pi$
$84$		0			0
$85$	−186.127			−0.237509
$86$	91.5908	+	158.640i	0.114843	+	0.198914i
$87$	−48.7599	+	84.4546i	−0.0600875	+	0.104075i
$88$	1883.35	−	3262.06i	2.28143	−	3.95155i
$89$	−22.8873	−	39.6420i	−0.0272590	−	0.0472139i	0.852074	−	0.523421i	$-0.175345\pi$
$89$	−22.8873	−	39.6420i	−0.0272590	−	0.0472139i	−0.879333	+	0.476207i	$0.842011\pi$
$90$	−143.848			−0.168477
$91$		0			0
$92$	550.607			0.623965
$93$	−732.426	−	1268.60i	−0.816657	−	1.41449i
$94$	−979.096	+	1695.84i	−1.07432	+	1.86078i
$95$	200.563	−	347.386i	0.216604	−	0.375169i
$96$	−1427.76	−	2472.95i	−1.51792	−	2.62911i
$97$	−1682.13			−1.76076			−0.880382	−	0.474265i	$-0.842714\pi$
$97$	−1682.13			−1.76076			−0.880382	+	0.474265i	$0.842714\pi$
$98$		0			0
$99$	277.667			0.281885
$100$	−266.421	−	461.455i	−0.266421	−	0.461455i
$101$	−217.083	+	375.999i	−0.213867	+	0.370429i	−0.952922	−	0.303217i	$-0.901939\pi$
$101$	−217.083	+	375.999i	−0.213867	+	0.370429i	0.739054	+	0.673646i	$0.235273\pi$
$102$	469.286	−	812.827i	0.455551	−	0.789038i
$103$	172.788	+	299.278i	0.165295	+	0.286299i	0.936760	−	0.349973i	$-0.113809\pi$
$103$	172.788	+	299.278i	0.165295	+	0.286299i	−0.771465	+	0.636272i	$0.780476\pi$
$104$	−2209.85			−2.08359
$105$		0			0
$106$	828.479			0.759142
$107$	−108.559	−	188.030i	−0.0980825	−	0.169884i	0.812808	−	0.582531i	$-0.197938\pi$
$107$	−108.559	−	188.030i	−0.0980825	−	0.169884i	−0.910891	+	0.412647i	$0.864604\pi$
$108$	1603.65	−	2777.60i	1.42880	−	2.47476i
$109$	−867.205	+	1502.04i	−0.762047	+	1.31990i	0.179746	+	0.983713i	$0.442472\pi$
$109$	−867.205	+	1502.04i	−0.762047	+	1.31990i	−0.941794	+	0.336192i	$0.890861\pi$
$110$	707.297	+	1225.07i	0.613074	+	1.06188i
$111$	918.086			0.785053
$112$		0			0
$113$	−1854.20			−1.54362			−0.771809	−	0.635855i	$-0.780648\pi$
$113$	−1854.20			−1.54362			−0.771809	+	0.635855i	$0.780648\pi$
$114$	1011.37	+	1751.74i	0.830907	+	1.43917i
$115$	−64.5837	+	111.862i	−0.0523692	+	0.0907062i
$116$	−223.167	+	386.536i	−0.178625	+	0.309387i
$117$	−81.4508	−	141.077i	−0.0643601	−	0.111475i
$118$	3335.16			2.60191
$119$		0			0
$120$	1678.41			1.27681
$121$	−699.784	−	1212.06i	−0.525758	−	0.910639i
$122$	41.3238	−	71.5749i	0.0306662	−	0.0531155i
$123$	26.4567	−	45.8244i	0.0193945	−	0.0335922i
$124$	−3352.20	−	5806.19i	−2.42772	−	4.20493i
$125$	125.000			0.0894427
$126$		0			0
$127$	1394.51			0.974352			0.487176	−	0.873304i	$-0.338027\pi$
$127$	1394.51			0.974352			0.487176	+	0.873304i	$0.338027\pi$
$128$	−1775.22	−	3074.78i	−1.22585	−	2.12324i
$129$	78.7788	−	136.449i	0.0537681	−	0.0931291i
$130$	414.957	−	718.726i	0.279955	−	0.484896i
$131$	881.209	+	1526.30i	0.587722	+	1.01796i	0.994530	+	0.104451i	$0.0333086\pi$
$131$	881.209	+	1526.30i	0.587722	+	1.01796i	−0.406808	+	0.913514i	$0.633358\pi$
$132$	−5186.54			−3.41993
$133$		0			0
$134$	−901.519			−0.581189
$135$	376.201	+	651.599i	0.239838	+	0.415412i
$136$	1341.66	−	2323.83i	0.845932	−	1.46520i
$137$	461.474	−	799.297i	0.287784	−	0.498457i	−0.685496	−	0.728076i	$-0.740415\pi$
$137$	461.474	−	799.297i	0.287784	−	0.498457i	0.973281	+	0.229619i	$0.0737481\pi$
$138$	−325.672	−	564.081i	−0.200892	−	0.347955i
$139$	196.039			0.119624			0.0598122	−	0.998210i	$-0.480950\pi$
$139$	196.039			0.119624			0.0598122	+	0.998210i	$0.480950\pi$
$140$		0			0
$141$	1684.27			1.00597
$142$	2577.17	+	4463.78i	1.52303	+	2.63797i
$143$	−800.984	+	1387.35i	−0.468403	+	0.811298i
$144$	583.882	−	1011.31i	0.337895	−	0.585251i
$145$	−52.3528	−	90.6777i	−0.0299839	−	0.0519336i
$146$	803.954			0.455724
$147$		0			0
$148$	4201.94			2.33376
$149$	−390.186	−	675.822i	−0.214532	−	0.371580i	0.738596	−	0.674149i	$-0.235489\pi$
$149$	−390.186	−	675.822i	−0.214532	−	0.371580i	−0.953128	+	0.302568i	$0.902156\pi$
$150$	−315.165	+	545.882i	−0.171554	+	0.297140i
$151$	1159.71	−	2008.68i	0.625008	−	1.08255i	−0.363531	−	0.931582i	$-0.618429\pi$
$151$	1159.71	−	2008.68i	0.625008	−	1.08255i	0.988539	−	0.150964i	$-0.0482377\pi$
$152$	2891.45	+	5008.15i	1.54295	+	2.67246i
$153$	197.805			0.104520
$154$		0			0
$155$	1572.79			0.815030
$156$	1521.42	+	2635.18i	0.780841	+	1.35246i
$157$	511.451	−	885.859i	0.259989	−	0.450314i	−0.706250	−	0.707963i	$-0.749615\pi$
$157$	511.451	−	885.859i	0.259989	−	0.450314i	0.966239	+	0.257649i	$0.0829478\pi$
$158$	−2321.95	+	4021.74i	−1.16914	+	2.02502i
$159$	−356.294	−	617.120i	−0.177711	−	0.307804i
$160$	3065.93			1.51489
$161$		0			0
$162$	−3017.31			−1.46335
$163$	675.313	+	1169.68i	0.324507	+	0.562062i	0.981412	−	0.191911i	$-0.0614684\pi$
$163$	675.313	+	1169.68i	0.324507	+	0.562062i	−0.656906	+	0.753973i	$0.728135\pi$
$164$	121.088	−	209.731i	0.0576549	−	0.0998613i
$165$	608.358	−	1053.71i	0.287034	−	0.497157i
$166$	1788.12	+	3097.12i	0.836054	+	1.44809i
$167$	1230.58			0.570209			0.285105	−	0.958496i	$-0.407972\pi$
$167$	1230.58			0.570209			0.285105	+	0.958496i	$0.407972\pi$
$168$		0			0
$169$	−1257.16			−0.572215
$170$	503.866	+	872.721i	0.227322	+	0.393733i
$171$	−213.147	+	369.182i	−0.0953203	+	0.165100i
$172$	360.558	−	624.506i	0.159839	−	0.276849i
$173$	−1243.83	−	2154.37i	−0.546626	−	0.946785i	−0.998503	−	0.0547040i	$-0.982578\pi$
$173$	−1243.83	−	2154.37i	−0.546626	−	0.946785i	0.451876	−	0.892081i	$-0.350755\pi$
$174$	527.993			0.230040
$175$		0			0
$176$	−11483.8			−4.91830
$177$	−1434.31	−	2484.30i	−0.609093	−	1.05498i
$178$	−123.917	+	214.630i	−0.0521795	+	0.0903776i
$179$	−810.589	+	1403.98i	−0.338471	+	0.586248i	−0.984145	−	0.177364i	$-0.943243\pi$
$179$	−810.589	+	1403.98i	−0.338471	+	0.586248i	0.645675	+	0.763613i	$0.276576\pi$
$180$	283.137	+	490.408i	0.117243	+	0.203071i
$181$	−2593.69			−1.06512			−0.532561	−	0.846392i	$-0.678770\pi$
$181$	−2593.69			−1.06512			−0.532561	+	0.846392i	$0.678770\pi$
$182$		0			0
$183$	−71.0866			−0.0287151
$184$	−931.081	−	1612.68i	−0.373044	−	0.646132i
$185$	−492.868	+	853.672i	−0.195872	+	0.339261i
$186$	−3965.51	+	6868.47i	−1.56326	+	2.70764i
$187$	−972.603	−	1684.60i	−0.380341	−	0.658770i
$188$	7708.66			2.99049
$189$		0			0
$190$	−2171.79			−0.829253
$191$	911.539	+	1578.83i	0.345323	+	0.598116i	0.985412	−	0.170184i	$-0.0544362\pi$
$191$	911.539	+	1578.83i	0.345323	+	0.598116i	−0.640090	+	0.768300i	$0.721103\pi$
$192$	−3636.54	+	6298.68i	−1.36690	+	2.36754i
$193$	770.514	−	1334.57i	0.287372	−	0.497743i	−0.685810	−	0.727781i	$-0.740552\pi$
$193$	770.514	−	1334.57i	0.287372	−	0.497743i	0.973182	+	0.230038i	$0.0738851\pi$
$194$	4553.70	+	7887.24i	1.68524	+	2.91892i
$195$	−713.823			−0.262143
$196$		0			0
$197$	701.243			0.253612			0.126806	−	0.991928i	$-0.459527\pi$
$197$	701.243			0.253612			0.126806	+	0.991928i	$0.459527\pi$
$198$	−751.674	−	1301.94i	−0.269794	−	0.467296i
$199$	1647.48	−	2853.52i	0.586868	−	1.01649i	−0.407771	−	0.913084i	$-0.633694\pi$
$199$	1647.48	−	2853.52i	0.586868	−	1.01649i	0.994640	−	0.103402i	$-0.0329727\pi$
$200$	−901.041	+	1560.65i	−0.318566	+	0.551773i
$201$	387.706	+	671.526i	0.136053	+	0.235651i
$202$	2350.67			0.818775
$203$		0			0
$204$	−3694.80			−1.26808
$205$	28.4062	+	49.2010i	0.00967793	+	0.0167627i
$206$	935.514	−	1620.36i	0.316409	−	0.548037i
$207$	68.6358	−	118.881i	0.0230460	−	0.0399168i
$208$	3368.64	+	5834.66i	1.12295	+	1.94501i
$209$	4192.16			1.38746
$210$		0			0
$211$	4082.35			1.33195			0.665974	−	0.745975i	$-0.268016\pi$
$211$	4082.35			1.33195			0.665974	+	0.745975i	$0.268016\pi$
$212$	−1630.70	−	2824.46i	−0.528289	−	0.915023i
$213$	2216.66	−	3839.37i	0.713067	−	1.23507i
$214$	−587.763	+	1018.04i	−0.187751	+	0.325194i
$215$	84.5837	+	146.503i	0.0268305	+	0.0464718i
$216$	−10847.1			−3.41691
$217$		0			0
$218$	9390.46			2.91744
$219$	−345.747	−	598.851i	−0.106682	−	0.184779i
$220$	2784.36	−	4822.65i	0.853280	−	1.47792i
$221$	−570.607	+	988.320i	−0.173679	+	0.300822i
$222$	−2485.36	−	4304.76i	−0.751379	−	1.30143i
$223$	−747.161			−0.224366			−0.112183	−	0.993688i	$-0.535784\pi$
$223$	−747.161			−0.224366			−0.112183	+	0.993688i	$0.535784\pi$
$224$		0			0
$225$	−132.843			−0.0393608
$226$	5019.53	+	8694.08i	1.47741	+	2.55894i
$227$	832.837	−	1442.52i	0.243513	−	0.421776i	−0.718200	−	0.695837i	$-0.755034\pi$
$227$	832.837	−	1442.52i	0.243513	−	0.421776i	0.961712	+	0.274061i	$0.0883670\pi$
$228$	3981.38	−	6895.95i	1.15646	−	2.00305i
$229$	−3314.18	−	5740.32i	−0.956362	−	1.65647i	−0.731219	−	0.682143i	$-0.761048\pi$
$229$	−3314.18	−	5740.32i	−0.956362	−	1.65647i	−0.225143	−	0.974326i	$-0.572285\pi$
$230$	699.340			0.200492
$231$		0			0
$232$	1509.50			0.427172
$233$	216.215	+	374.496i	0.0607929	+	0.105296i	0.894820	−	0.446427i	$-0.147304\pi$
$233$	216.215	+	374.496i	0.0607929	+	0.105296i	−0.834027	+	0.551723i	$0.813970\pi$
$234$	−440.992	+	763.821i	−0.123199	+	0.213387i
$235$	−904.190	+	1566.10i	−0.250991	+	0.434729i
$236$	−6564.62	−	11370.3i	−1.81068	−	3.13619i
$237$	3994.30			1.09476
$238$		0			0
$239$	5580.44			1.51033			0.755165	−	0.655535i	$-0.227557\pi$
$239$	5580.44			1.51033			0.755165	+	0.655535i	$0.227557\pi$
$240$	−2558.53	−	4431.50i	−0.688135	−	1.19188i
$241$	−3148.43	+	5453.25i	−0.841529	+	1.45757i	0.0470730	+	0.998891i	$0.485011\pi$
$241$	−3148.43	+	5453.25i	−0.841529	+	1.45757i	−0.888602	+	0.458679i	$0.848323\pi$
$242$	−3788.78	+	6562.36i	−1.00641	+	1.74316i
$243$	−733.864	−	1271.09i	−0.193734	−	0.335557i
$244$	−325.352			−0.0853629
$245$		0			0
$246$	−286.485			−0.0742504
$247$	−1229.73	−	2129.95i	−0.316785	−	0.548687i
$248$	−11337.2	+	19636.6i	−2.90287	+	5.02793i
$249$	1537.99	−	2663.88i	0.391431	−	0.677978i
$250$	−338.388	−	586.106i	−0.0856062	−	0.148274i
$251$	−311.921			−0.0784393			−0.0392197	−	0.999231i	$-0.512487\pi$
$251$	−311.921			−0.0784393			−0.0392197	+	0.999231i	$0.512487\pi$
$252$		0			0
$253$	−1349.92			−0.335451
$254$	−3775.09	−	6538.64i	−0.932559	−	1.61524i
$255$	433.383	−	750.642i	0.106429	−	0.184341i
$256$	−3364.23	+	5827.02i	−0.821346	+	1.42261i
$257$	−3930.69	−	6808.16i	−0.954046	−	1.65246i	−0.736535	−	0.676399i	$-0.763539\pi$
$257$	−3930.69	−	6808.16i	−0.954046	−	1.65246i	−0.217511	−	0.976058i	$-0.569794\pi$
$258$	−853.050			−0.205847
$259$		0			0
$260$	−3267.06			−0.779285
$261$	55.6375	+	96.3670i	0.0131949	+	0.0228543i
$262$	4771.06	−	8263.71i	1.12503	−	1.94860i
$263$	−2613.55	+	4526.80i	−0.612769	+	1.06135i	0.378003	+	0.925804i	$0.376611\pi$
$263$	−2613.55	+	4526.80i	−0.612769	+	1.06135i	−0.990772	+	0.135542i	$0.956722\pi$
$264$	8770.48	+	15190.9i	2.04464	+	3.54143i
$265$	765.097			0.177357
$266$		0			0
$267$	213.166			0.0488596
$268$	1774.47	+	3073.47i	0.404451	+	0.700530i
$269$	640.854	−	1109.99i	0.145255	−	0.251589i	−0.784213	−	0.620491i	$-0.786933\pi$
$269$	640.854	−	1109.99i	0.145255	−	0.251589i	0.929468	+	0.368903i	$0.120266\pi$
$270$	2036.83	−	3527.89i	0.459102	−	0.795188i
$271$	2352.07	+	4073.91i	0.527226	+	0.913182i	0.999497	+	0.0317282i	$0.0101011\pi$
$271$	2352.07	+	4073.91i	0.527226	+	0.913182i	−0.472271	+	0.881453i	$0.656566\pi$
$272$	−8180.82			−1.82366
$273$		0			0
$274$	−4997.04			−1.10176
$275$	653.185	+	1131.35i	0.143231	+	0.248084i
$276$	−1282.05	+	2220.57i	−0.279602	+	0.484286i
$277$	−4479.28	+	7758.34i	−0.971603	+	1.68286i	−0.280883	+	0.959742i	$0.590627\pi$
$277$	−4479.28	+	7758.34i	−0.971603	+	1.68286i	−0.690719	+	0.723123i	$0.742706\pi$
$278$	−530.698	−	919.195i	−0.114493	−	0.198308i
$279$	−1671.47			−0.358668
$280$		0			0
$281$	−370.904			−0.0787412			−0.0393706	−	0.999225i	$-0.512535\pi$
$281$	−370.904			−0.0787412			−0.0393706	+	0.999225i	$0.512535\pi$
$282$	−4559.51	−	7897.30i	−0.962818	−	1.66765i
$283$	−2911.13	+	5042.22i	−0.611479	+	1.05911i	0.379512	+	0.925187i	$0.376092\pi$
$283$	−2911.13	+	5042.22i	−0.611479	+	1.05911i	−0.990991	+	0.133926i	$0.957241\pi$
$284$	10145.3	−	17572.2i	2.11977	−	3.67155i
$285$	933.995	+	1617.73i	0.194123	+	0.336231i
$286$	8673.40			1.79325
$287$		0			0
$288$	−3258.29			−0.666655
$289$	1763.63	+	3054.71i	0.358973	+	0.621760i
$290$	−283.449	+	490.949i	−0.0573956	+	0.0994121i
$291$	3916.71	−	6783.94i	0.789009	−	1.36660i
$292$	−1582.43	−	2740.85i	−0.317140	−	0.549302i
$293$	−7443.79			−1.48420			−0.742100	−	0.670289i	$-0.766170\pi$
$293$	−7443.79			−1.48420			−0.742100	+	0.670289i	$0.766170\pi$
$294$		0			0
$295$	3080.00			0.607880
$296$	−7105.51	−	12307.1i	−1.39527	−	2.41667i
$297$	−3931.66	+	6809.83i	−0.768142	+	1.33046i
$298$	−2112.55	+	3659.04i	−0.410660	+	0.711284i
$299$	395.987	+	685.869i	0.0765903	+	0.132658i
$300$	2481.37			0.477540
$301$		0			0
$302$	−12557.9			−2.39280
$303$	−1010.93	−	1750.97i	−0.191670	−	0.331983i
$304$	8815.35	−	15268.6i	1.66314	−	2.88064i
$305$	38.1623	−	66.0991i	0.00716449	−	0.0124093i
$306$	−535.479	−	927.477i	−0.100037	−	0.173269i
$307$	761.674			0.141600			0.0707998	−	0.997491i	$-0.477445\pi$
$307$	761.674			0.141600			0.0707998	+	0.997491i	$0.477445\pi$
$308$		0			0
$309$	−1609.30			−0.296278
$310$	−4257.72	−	7374.58i	−0.780071	−	1.35112i
$311$	3859.35	−	6684.58i	0.703677	−	1.21880i	−0.263490	−	0.964662i	$-0.584874\pi$
$311$	3859.35	−	6684.58i	0.703677	−	1.21880i	0.967167	−	0.254142i	$-0.0817929\pi$
$312$	5145.47	−	8912.21i	0.933669	−	1.61716i
$313$	4278.00	+	7409.72i	0.772546	+	1.33809i	0.936163	+	0.351565i	$0.114350\pi$
$313$	4278.00	+	7409.72i	0.772546	+	1.33809i	−0.163617	+	0.986524i	$0.552316\pi$
$314$	−5538.21			−0.995348
$315$		0			0
$316$	18281.3			3.25444
$317$	3890.48	+	6738.50i	0.689309	+	1.19392i	0.972062	+	0.234725i	$0.0754189\pi$
$317$	3890.48	+	6738.50i	0.689309	+	1.19392i	−0.282753	+	0.959193i	$0.591248\pi$
$318$	−1929.05	+	3341.22i	−0.340176	+	0.589202i
$319$	547.138	−	947.670i	0.0960308	−	0.166330i
$320$	−3904.51	−	6762.81i	−0.682089	−	1.18141i
$321$	1011.09			0.175805
$322$		0			0
$323$	2986.42			0.514455
$324$	5939.00	+	10286.7i	1.01835	+	1.76383i
$325$	383.211	−	663.740i	0.0654052	−	0.113285i
$326$	3656.29	−	6332.88i	0.621175	−	1.07591i
$327$	−4038.45	−	6994.79i	−0.682956	−	1.18291i
$328$	−819.045			−0.137879
$329$		0			0
$330$	−6587.56			−1.09889
$331$	2466.06	+	4271.34i	0.409507	+	0.709288i	0.994835	−	0.101510i	$-0.0323673\pi$
$331$	2466.06	+	4271.34i	0.409507	+	0.709288i	−0.585327	+	0.810797i	$0.699034\pi$
$332$	7039.15	−	12192.2i	1.16363	−	2.01546i
$333$	523.791	−	907.233i	0.0861970	−	0.149298i
$334$	−3331.31	−	5769.99i	−0.545751	−	0.945269i
$335$	−832.548			−0.135782
$336$		0			0
$337$	−7121.13			−1.15108			−0.575538	−	0.817775i	$-0.695207\pi$
$337$	−7121.13			−1.15108			−0.575538	+	0.817775i	$0.695207\pi$
$338$	3403.26	+	5894.62i	0.547671	+	0.948594i
$339$	4317.38	−	7477.92i	0.691704	−	1.19807i
$340$	1983.53	−	3435.57i	0.316388	−	0.548000i
$341$	8218.60	+	14235.0i	1.30517	+	2.26062i
$342$	2308.05			0.364927
$343$		0			0
$344$	−2438.83			−0.382246
$345$	−300.757	−	520.926i	−0.0469339	−	0.0812919i
$346$	−6734.34	+	11664.2i	−1.04636	+	1.81235i
$347$	−4770.29	+	8262.39i	−0.737991	+	1.27824i	0.215408	+	0.976524i	$0.430892\pi$
$347$	−4770.29	+	8262.39i	−0.737991	+	1.27824i	−0.953399	+	0.301713i	$0.902442\pi$
$348$	−1039.25	−	1800.04i	−0.160086	−	0.277277i
$349$	−1281.65			−0.196576			−0.0982880	−	0.995158i	$-0.531337\pi$
$349$	−1281.65			−0.196576			−0.0982880	+	0.995158i	$0.531337\pi$
$350$		0			0
$351$	4613.25			0.701530
$352$	16021.0	+	27749.1i	2.42591	+	4.20180i
$353$	2899.03	−	5021.27i	0.437110	−	0.757097i	−0.560355	−	0.828253i	$-0.689335\pi$
$353$	2899.03	−	5021.27i	0.437110	−	0.757097i	0.997465	+	0.0711552i	$0.0226686\pi$
$354$	−7765.67	+	13450.5i	−1.16593	+	2.01946i
$355$	2380.00	+	4122.28i	0.355823	+	0.616304i
$356$	975.627			0.145247
$357$		0			0
$358$	8777.40			1.29581
$359$	−1133.65	−	1963.53i	−0.166662	−	0.288666i	0.770583	−	0.637340i	$-0.219965\pi$
$359$	−1133.65	−	1963.53i	−0.166662	−	0.288666i	−0.937244	+	0.348674i	$0.886632\pi$
$360$	957.574	−	1658.57i	0.140190	−	0.242817i
$361$	211.443	−	366.230i	0.0308271	−	0.0533940i
$362$	7021.38	+	12161.4i	1.01944	+	1.76571i
$363$	6517.58			0.942381
$364$		0			0
$365$	742.447			0.106470
$366$	192.439	+	333.314i	0.0274835	+	0.0476027i
$367$	−3686.42	+	6385.07i	−0.524332	+	0.908169i	0.475267	+	0.879842i	$0.342351\pi$
$367$	−3686.42	+	6385.07i	−0.524332	+	0.908169i	−0.999599	+	0.0283274i	$0.990982\pi$
$368$	−2838.64	+	4916.67i	−0.402104	+	0.696465i
$369$	−30.1885	−	52.2879i	−0.00425894	−	0.00737670i
$370$	5336.98			0.749883
$371$		0			0
$372$	31221.4			4.35150
$373$	−3223.57	−	5583.39i	−0.447480	−	0.775059i	0.550741	−	0.834676i	$-0.314345\pi$
$373$	−3223.57	−	5583.39i	−0.447480	−	0.775059i	−0.998221	+	0.0596176i	$0.981012\pi$
$374$	−5265.88	+	9120.78i	−0.728054	+	1.26103i
$375$	−291.053	+	504.119i	−0.0400798	+	0.0694203i
$376$	−13035.4	−	22578.0i	−1.78790	−	3.09673i
$377$	−641.989			−0.0877032
$378$		0			0
$379$	−4247.57			−0.575680			−0.287840	−	0.957678i	$-0.592937\pi$
$379$	−4247.57			−0.575680			−0.287840	+	0.957678i	$0.592937\pi$
$380$	4274.75	+	7404.09i	0.577079	+	0.999531i
$381$	−3247.01	+	5623.99i	−0.436613	+	0.756236i
$382$	4935.27	−	8548.13i	0.661021	−	1.14492i
$383$	−3340.93	−	5786.66i	−0.445727	−	0.772022i	0.552375	−	0.833595i	$-0.313721\pi$
$383$	−3340.93	−	5786.66i	−0.445727	−	0.772022i	−0.998103	+	0.0615735i	$0.980388\pi$
$384$	16533.9			2.19725
$385$		0			0
$386$	−8343.45			−1.10018
$387$	−89.8906	−	155.695i	−0.0118072	−	0.0204507i
$388$	17926.2	−	31049.1i	2.34553	−	4.06257i
$389$	3185.89	−	5518.12i	0.415247	−	0.719229i	−0.580207	−	0.814469i	$-0.697029\pi$
$389$	3185.89	−	5518.12i	0.415247	−	0.719229i	0.995454	+	0.0952400i	$0.0303619\pi$
$390$	1932.39	+	3347.00i	0.250899	+	0.434570i
$391$	−961.661			−0.124382
$392$		0			0
$393$	−8207.33			−1.05345
$394$	−1898.34	−	3288.02i	−0.242733	−	0.420427i
$395$	−2144.31	+	3714.06i	−0.273144	+	0.473100i
$396$	−2959.06	+	5125.24i	−0.375500	+	0.650386i
$397$	2123.96	+	3678.81i	0.268510	+	0.465074i	0.968477	−	0.249101i	$-0.0801353\pi$
$397$	2123.96	+	3678.81i	0.268510	+	0.465074i	−0.699967	+	0.714175i	$0.746802\pi$
$398$	−17839.6			−2.24678
$399$		0			0
$400$	5494.11			0.686764
$401$	4416.81	+	7650.14i	0.550038	+	0.952693i	0.998271	+	0.0587765i	$0.0187199\pi$
$401$	4416.81	+	7650.14i	0.550038	+	0.952693i	−0.448234	+	0.893916i	$0.647947\pi$
$402$	2099.12	−	3635.78i	0.260434	−	0.451086i
$403$	4821.69	−	8351.41i	0.595993	−	1.03229i
$404$	−4626.85	−	8013.94i	−0.569788	−	0.986902i
$405$	−2786.47			−0.341879
$406$		0			0
$407$	−10301.9			−1.25466
$408$	6247.93	+	10821.7i	0.758134	+	1.31313i
$409$	−159.602	+	276.439i	−0.0192954	+	0.0334206i	−0.875512	−	0.483197i	$-0.839476\pi$
$409$	−159.602	+	276.439i	−0.0192954	+	0.0334206i	0.856216	+	0.516617i	$0.172809\pi$
$410$	153.797	−	266.385i	0.0185256	−	0.0320873i
$411$	2149.02	+	3722.21i	0.257916	+	0.446723i
$412$	−7365.53			−0.880761
$413$		0			0
$414$	−743.218			−0.0882298
$415$	1651.32	+	2860.17i	0.195326	+	0.338314i
$416$	9399.17	−	16279.8i	1.10777	−	1.91871i
$417$	−456.462	+	790.615i	−0.0536044	+	0.0928455i
$418$	−11348.6	−	19656.4i	−1.32794	−	2.30006i
$419$	12789.2			1.49115			0.745577	−	0.666420i	$-0.232174\pi$
$419$	12789.2			1.49115			0.745577	+	0.666420i	$0.232174\pi$
$420$		0			0
$421$	−6747.40			−0.781112			−0.390556	−	0.920579i	$-0.627717\pi$
$421$	−6747.40			−0.781112			−0.390556	+	0.920579i	$0.627717\pi$
$422$	−11051.4	−	19141.5i	−1.27482	−	2.20805i
$423$	960.921	−	1664.36i	0.110453	−	0.191310i
$424$	−5515.07	+	9552.38i	−0.631687	+	1.09411i
$425$	465.317	+	805.953i	0.0531087	+	0.0919870i
$426$	−24003.0			−2.72992
$427$		0			0
$428$	4627.60			0.522625
$429$	−3730.07	−	6460.67i	−0.419789	−	0.727095i
$430$	457.954	−	793.200i	0.0513593	−	0.0889570i
$431$	2592.37	−	4490.12i	0.289722	−	0.501813i	−0.684021	−	0.729462i	$-0.739770\pi$
$431$	2592.37	−	4490.12i	0.289722	−	0.501813i	0.973743	+	0.227649i	$0.0731038\pi$
$432$	16535.1	+	28639.6i	1.84154	+	3.18964i
$433$	4242.03			0.470806			0.235403	−	0.971898i	$-0.424359\pi$
$433$	4242.03			0.470806			0.235403	+	0.971898i	$0.424359\pi$
$434$		0			0
$435$	487.599			0.0537439
$436$	−18483.3	−	32014.1i	−2.03026	−	3.51651i
$437$	1036.25	−	1794.84i	0.113434	−	0.196473i
$438$	−1871.95	+	3242.31i	−0.204213	+	0.353707i
$439$	−2717.06	−	4706.08i	−0.295394	−	0.511638i	0.679682	−	0.733507i	$-0.262118\pi$
$439$	−2717.06	−	4706.08i	−0.295394	−	0.511638i	−0.975077	+	0.221869i	$0.928784\pi$
$440$	−18833.5			−2.04057
$441$		0			0
$442$	6178.77			0.664919
$443$	5746.89	+	9953.91i	0.616350	+	1.06755i	0.990146	+	0.140039i	$0.0447228\pi$
$443$	5746.89	+	9953.91i	0.616350	+	1.06755i	−0.373796	+	0.927511i	$0.621944\pi$
$444$	−9783.91	+	16946.2i	−1.04577	+	1.81133i
$445$	−114.437	+	198.210i	−0.0121906	+	0.0211147i
$446$	2022.65	+	3503.32i	0.214742	+	0.371944i
$447$	3634.08			0.384532
$448$		0			0
$449$	−16849.3			−1.77098			−0.885489	−	0.464661i	$-0.846176\pi$
$449$	−16849.3			−1.77098			−0.885489	+	0.464661i	$0.846176\pi$
$450$	359.619	+	622.879i	0.0376725	+	0.0652507i
$451$	−296.872	+	514.198i	−0.0309959	+	0.0536865i
$452$	19760.0	−	34225.3i	2.05626	−	3.56155i
$453$	5400.62	+	9354.15i	0.560140	+	0.970191i
$454$	−9018.32			−0.932270
$455$		0			0
$456$	−26930.2			−2.76561
$457$	−7674.25	−	13292.2i	−0.785528	−	1.36057i	−0.928683	−	0.370875i	$-0.879058\pi$
$457$	−7674.25	−	13292.2i	−0.785528	−	1.36057i	0.143155	−	0.989700i	$-0.454275\pi$
$458$	−17943.7	+	31079.3i	−1.83068	+	3.17083i
$459$	−2800.84	+	4851.20i	−0.284820	+	0.493322i
$460$	−1376.52	−	2384.20i	−0.139523	−	0.241661i
$461$	−14038.4			−1.41830			−0.709148	−	0.705059i	$-0.750920\pi$
$461$	−14038.4			−1.41830			−0.709148	+	0.705059i	$0.750920\pi$
$462$		0			0
$463$	−8661.23			−0.869377			−0.434689	−	0.900581i	$-0.643142\pi$
$463$	−8661.23			−0.869377			−0.434689	+	0.900581i	$0.643142\pi$
$464$	−2301.06	−	3985.55i	−0.230224	−	0.398760i
$465$	−3662.13	+	6343.00i	−0.365220	+	0.632580i
$466$	1170.64	−	2027.60i	0.116371	−	0.201560i
$467$	3507.35	+	6074.91i	0.347539	+	0.601956i	0.985812	−	0.167855i	$-0.0536839\pi$
$467$	3507.35	+	6074.91i	0.347539	+	0.601956i	−0.638272	+	0.769811i	$0.720351\pi$
$468$	3472.04			0.342938
$469$		0			0
$470$	9790.96			0.960901
$471$	2381.75	+	4125.32i	0.233005	+	0.403576i
$472$	−22201.6	+	38454.4i	−2.16507	+	3.75001i
$473$	−883.981	+	1531.10i	−0.0859313	+	0.148837i
$474$	−10813.0	−	18728.7i	−1.04780	−	1.81484i
$475$	−2005.63			−0.193737
$476$		0			0
$477$	−813.100			−0.0780488
$478$	−15106.9	−	26165.8i	−1.44555	−	2.50376i
$479$	9067.34	−	15705.1i	0.864922	−	1.49809i	−0.00220344	−	0.999998i	$-0.500701\pi$
$479$	9067.34	−	15705.1i	0.864922	−	1.49809i	0.867125	−	0.498091i	$-0.165965\pi$
$480$	−7138.79	+	12364.8i	−0.678833	+	1.17577i
$481$	3021.96	+	5234.18i	0.286464	+	0.496171i
$482$	34092.6			3.22173
$483$		0			0
$484$	29830.0			2.80146
$485$	4205.32	+	7283.82i	0.393719	+	0.681941i
$486$	−3973.30	+	6881.95i	−0.370848	+	0.642328i
$487$	−8268.92	+	14322.2i	−0.769405	+	1.33265i	0.168480	+	0.985705i	$0.446114\pi$
$487$	−8268.92	+	14322.2i	−0.769405	+	1.33265i	−0.937886	+	0.346944i	$0.887219\pi$
$488$	550.173	+	952.928i	0.0510352	+	0.0883955i
$489$	−6289.67			−0.581654
$490$		0			0
$491$	220.608			0.0202768			0.0101384	−	0.999949i	$-0.496773\pi$
$491$	220.608			0.0202768			0.0101384	+	0.999949i	$0.496773\pi$
$492$	563.891	+	976.687i	0.0516710	+	0.0894969i
$493$	389.771	−	675.103i	0.0356073	−	0.0616736i
$494$	−6658.02	+	11532.0i	−0.606393	+	1.05030i
$495$	−694.167	−	1202.33i	−0.0630313	−	0.109173i
$496$	69128.8			6.25801
$497$		0			0
$498$	−16654.0			−1.49856
$499$	−2969.52	−	5143.36i	−0.266401	−	0.461419i	0.701529	−	0.712641i	$-0.252501\pi$
$499$	−2969.52	−	5143.36i	−0.266401	−	0.461419i	−0.967930	+	0.251222i	$0.919168\pi$
$500$	−1332.11	+	2307.28i	−0.119147	+	0.206369i
$501$	−2865.31	+	4962.86i	−0.255514	+	0.442564i
$502$	844.403	+	1462.55i	0.0750748	+	0.130033i
$503$	11604.8			1.02869			0.514345	−	0.857584i	$-0.328035\pi$
$503$	11604.8			1.02869			0.514345	+	0.857584i	$0.328035\pi$
$504$		0			0
$505$	2170.83			0.191289
$506$	3654.39	+	6329.59i	0.321062	+	0.556096i
$507$	2927.20	−	5070.06i	0.256413	−	0.444121i
$508$	−14861.1	+	25740.2i	−1.29794	+	2.24810i
$509$	−933.836	−	1617.45i	−0.0813193	−	0.140849i	0.822498	−	0.568769i	$-0.192580\pi$
$509$	−933.836	−	1617.45i	−0.0813193	−	0.140849i	−0.903817	+	0.427919i	$0.859247\pi$
$510$	−4692.86			−0.407457
$511$		0			0
$512$	8025.75			0.692757
$513$	−6036.17	−	10454.9i	−0.519500	−	0.899800i
$514$	−21281.6	+	36860.8i	−1.82625	+	3.16316i
$515$	863.942	−	1496.39i	0.0739220	−	0.128037i
$516$	1679.07	+	2908.23i	0.143250	+	0.248116i
$517$	−18899.3			−1.60772
$518$		0			0
$519$	11584.6			0.979786
$520$	5524.62	+	9568.91i	0.465905	+	0.806970i
$521$	3058.60	−	5297.66i	0.257197	−	0.445479i	−0.708293	−	0.705919i	$-0.750534\pi$
$521$	3058.60	−	5297.66i	0.257197	−	0.445479i	0.965490	+	0.260440i	$0.0838676\pi$
$522$	301.233	−	521.752i	0.0252579	−	0.0437480i
$523$	−8342.80	−	14450.2i	−0.697524	−	1.20815i	−0.969322	−	0.245793i	$-0.920952\pi$
$523$	−8342.80	−	14450.2i	−0.697524	−	1.20815i	0.271798	−	0.962354i	$-0.412382\pi$
$524$	−37563.7			−3.13164
$525$		0			0
$526$	28300.6			2.34594
$527$	5854.78	+	10140.8i	0.483944	+	0.838215i
$528$	26739.1	−	46313.5i	2.20392	−	3.81730i
$529$	5749.82	−	9958.97i	0.472575	−	0.818523i
$530$	−2071.20	−	3587.42i	−0.169749	−	0.294014i
$531$	−3273.24			−0.267508
$532$		0			0
$533$	348.338			0.0283081
$534$	−577.062	−	999.501i	−0.0467639	−	0.0809975i
$535$	−542.797	+	940.151i	−0.0438638	+	0.0759744i
$536$	6001.28	−	10394.5i	0.483612	−	0.837640i
$537$	−3774.79	−	6538.13i	−0.303341	−	0.525403i
$538$	−6939.44			−0.556097
$539$		0			0
$540$	−16036.5			−1.27796
$541$	−4654.51	−	8061.86i	−0.369895	−	0.640677i	0.619654	−	0.784875i	$-0.287273\pi$
$541$	−4654.51	−	8061.86i	−0.369895	−	0.640677i	−0.989549	+	0.144198i	$0.953940\pi$
$542$	12734.6	−	22057.0i	1.00922	−	1.74802i
$543$	6039.21	−	10460.2i	0.477288	−	0.826686i
$544$	11413.0	+	19768.0i	0.899504	+	1.55799i
$545$	8672.05			0.681596
$546$		0			0
$547$	10894.7			0.851598			0.425799	−	0.904818i	$-0.359993\pi$
$547$	10894.7			0.851598			0.425799	+	0.904818i	$0.359993\pi$
$548$	9835.73	+	17036.0i	0.766718	+	1.32799i
$549$	−40.5567	+	70.2463i	−0.00315286	+	0.00546091i
$550$	3536.49	−	6125.37i	0.274175	−	0.474885i
$551$	840.005	+	1454.93i	0.0649463	+	0.112490i
$552$	8671.81			0.668654
$553$		0			0
$554$	48503.6			3.71971
$555$	−2295.21	−	3975.43i	−0.175543	−	0.304050i
$556$	−2089.16	+	3618.52i	−0.159352	+	0.276006i
$557$	3936.95	−	6818.99i	0.299486	−	0.518725i	−0.676532	−	0.736413i	$-0.736518\pi$
$557$	3936.95	−	6818.99i	0.299486	−	0.518725i	0.976019	+	0.217688i	$0.0698514\pi$
$558$	4524.85	+	7837.27i	0.343284	+	0.594585i
$559$	1037.23			0.0784796
$560$		0			0
$561$	9058.55			0.681733
$562$	1004.08	+	1739.11i	0.0753638	+	0.130534i
$563$	10885.4	−	18854.0i	0.814854	−	1.41137i	−0.0945786	−	0.995517i	$-0.530150\pi$
$563$	10885.4	−	18854.0i	0.814854	−	1.41137i	0.909433	−	0.415851i	$-0.136516\pi$
$564$	−17949.1	+	31088.7i	−1.34006	+	2.32105i
$565$	4635.51	+	8028.94i	0.345163	+	0.597841i
$566$	31522.9			2.34100
$567$		0			0
$568$	−68623.3			−5.06931
$569$	6190.63	+	10722.5i	0.456106	+	0.790000i	0.998751	−	0.0499628i	$-0.0159103\pi$
$569$	6190.63	+	10722.5i	0.456106	+	0.790000i	−0.542645	+	0.839962i	$0.682577\pi$
$570$	5056.85	−	8758.72i	0.371593	−	0.643618i
$571$	2884.19	−	4995.56i	0.211383	−	0.366126i	−0.740765	−	0.671764i	$-0.765537\pi$
$571$	2884.19	−	4995.56i	0.211383	−	0.366126i	0.952148	+	0.305639i	$0.0988700\pi$
$572$	−17071.9	−	29569.5i	−1.24793	−	2.16147i
$573$	−8489.81			−0.618965
$574$		0			0
$575$	645.837			0.0468405
$576$	4149.48	+	7187.12i	0.300165	+	0.519901i
$577$	2366.69	−	4099.23i	0.170757	−	0.295759i	−0.767928	−	0.640536i	$-0.778712\pi$
$577$	2366.69	−	4099.23i	0.170757	−	0.295759i	0.938685	+	0.344777i	$0.112045\pi$
$578$	9548.70	−	16538.8i	0.687151	−	1.19018i
$579$	3588.17	+	6214.89i	0.257546	+	0.446083i
$580$	2231.67			0.159767
$581$		0			0
$582$	−42411.8			−3.02066
$583$	3998.00	+	6924.74i	0.284014	+	0.491927i
$584$	−5351.80	+	9269.59i	−0.379211	+	0.656813i
$585$	−407.254	+	705.385i	−0.0287827	+	0.0498531i
$586$	20151.1	+	34902.8i	1.42054	+	2.46044i
$587$	8441.67			0.593569			0.296785	−	0.954944i	$-0.404086\pi$
$587$	8441.67			0.593569			0.296785	+	0.954944i	$0.404086\pi$
$588$		0			0
$589$	−25235.6			−1.76539
$590$	−8337.89	−	14441.6i	−0.581806	−	1.00772i
$591$	−1632.79	+	2828.08i	−0.113645	+	0.196839i
$592$	−21663.0	+	37521.4i	−1.50396	+	2.60493i
$593$	9469.94	+	16402.4i	0.655791	+	1.13586i	0.981695	+	0.190460i	$0.0609979\pi$
$593$	9469.94	+	16402.4i	0.655791	+	1.13586i	−0.325904	+	0.945403i	$0.605669\pi$
$594$	42573.7			2.94077
$595$		0			0
$596$	16632.6			1.14312
$597$	7672.08	+	13288.4i	0.525958	+	0.910987i
$598$	2143.96	−	3713.44i	0.146610	−	0.253936i
$599$	−11327.7	+	19620.1i	−0.772681	+	1.33832i	0.163407	+	0.986559i	$0.447752\pi$
$599$	−11327.7	+	19620.1i	−0.772681	+	1.33832i	−0.936089	+	0.351764i	$0.885582\pi$
$600$	−4196.02	−	7267.71i	−0.285503	−	0.494505i
$601$	15947.4			1.08237			0.541187	−	0.840902i	$-0.317975\pi$
$601$	15947.4			1.08237			0.541187	+	0.840902i	$0.317975\pi$
$602$		0			0
$603$	884.784			0.0597532
$604$	24717.8	+	42812.5i	1.66516	+	2.88413i
$605$	−3498.92	+	6060.31i	−0.235126	+	0.407250i
$606$	−5473.36	+	9480.15i	−0.366898	+	0.635486i
$607$	−12996.6	−	22510.8i	−0.869053	−	1.50524i	−0.862966	−	0.505263i	$-0.831396\pi$
$607$	−12996.6	−	22510.8i	−0.869053	−	1.50524i	−0.00608748	−	0.999981i	$-0.501938\pi$
$608$	−49193.1			−3.28132
$609$		0			0
$610$	−413.238			−0.0274287
$611$	5543.93	+	9602.36i	0.367076	+	0.635794i
$612$	−2107.98	+	3651.13i	−0.139232	+	0.241157i
$613$	−332.704	+	576.260i	−0.0219213	+	0.0379689i	−0.876778	−	0.480895i	$-0.840312\pi$
$613$	−332.704	+	576.260i	−0.0219213	+	0.0379689i	0.854857	+	0.518864i	$0.173645\pi$
$614$	−2061.93	−	3571.37i	−0.135526	−	0.234738i
$615$	−264.567			−0.0173470
$616$		0			0
$617$	18401.3			1.20066			0.600330	−	0.799752i	$-0.295036\pi$
$617$	18401.3			1.20066			0.600330	+	0.799752i	$0.295036\pi$
$618$	4356.55	+	7545.77i	0.283570	+	0.491157i
$619$	−5575.30	+	9656.70i	−0.362020	+	0.627037i	−0.988293	−	0.152567i	$-0.951246\pi$
$619$	−5575.30	+	9656.70i	−0.362020	+	0.627037i	0.626273	+	0.779604i	$0.284579\pi$
$620$	−16761.0	+	29030.9i	−1.08571	+	1.88050i
$621$	1943.71	+	3366.61i	0.125602	+	0.217548i
$622$	−41790.6			−2.69397
$623$		0			0
$624$	−31374.6			−2.01280
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	23162.0	−	40117.8i	1.47882	−	2.56139i
$627$	−9761.15	+	16906.8i	−0.621727	+	1.07686i
$628$	10900.9	+	18880.9i	0.692665	+	1.19973i
$629$	−7338.88			−0.465215
$630$		0			0
$631$	5381.79			0.339534			0.169767	−	0.985484i	$-0.445699\pi$
$631$	5381.79			0.339534			0.169767	+	0.985484i	$0.445699\pi$
$632$	−30913.8	−	53544.3i	−1.94570	−	3.37006i
$633$	−9505.46	+	16463.9i	−0.596854	+	1.03378i
$634$	21063.9	−	36483.7i	1.31948	−	2.28541i
$635$	−3486.27	−	6038.40i	−0.217872	−	0.377365i
$636$	15187.9			0.946918
$637$		0			0
$638$	−5924.64			−0.367647
$639$	−2529.33	−	4380.92i	−0.156586	−	0.271215i
$640$	−8876.12	+	15373.9i	−0.548218	+	0.949542i
$641$	9727.53	−	16848.6i	0.599398	−	1.03819i	−0.393512	−	0.919320i	$-0.628740\pi$
$641$	9727.53	−	16848.6i	0.599398	−	1.03819i	0.992910	−	0.118869i	$-0.0379267\pi$
$642$	−2737.13	−	4740.84i	−0.168265	−	0.291443i
$643$	14695.8			0.901317			0.450658	−	0.892696i	$-0.351189\pi$
$643$	14695.8			0.901317			0.450658	+	0.892696i	$0.351189\pi$
$644$		0			0
$645$	−787.788			−0.0480917
$646$	−8084.56	−	14002.9i	−0.492388	−	0.852842i
$647$	−6347.41	+	10994.0i	−0.385691	+	0.668037i	−0.991865	−	0.127295i	$-0.959370\pi$
$647$	−6347.41	+	10994.0i	−0.385691	+	0.668037i	0.606174	+	0.795332i	$0.292704\pi$
$648$	20085.8	−	34789.6i	1.21766	−	2.10905i
$649$	16094.5	+	27876.5i	0.973442	+	1.68605i
$650$	−4149.57			−0.250399
$651$		0			0
$652$	−28786.8			−1.72911
$653$	6192.82	+	10726.3i	0.371124	+	0.642805i	0.989739	−	0.142889i	$-0.0456393\pi$
$653$	6192.82	+	10726.3i	0.371124	+	0.642805i	−0.618615	+	0.785694i	$0.712306\pi$
$654$	−21865.0	+	37871.3i	−1.30732	+	2.26435i
$655$	4406.05	−	7631.50i	0.262837	−	0.455248i
$656$	1248.54	+	2162.53i	0.0743096	+	0.128708i
$657$	−789.030			−0.0468539
$658$		0			0
$659$	−2072.18			−0.122489			−0.0612447	−	0.998123i	$-0.519507\pi$
$659$	−2072.18			−0.122489			−0.0612447	+	0.998123i	$0.519507\pi$
$660$	12966.4	+	22458.4i	0.764720	+	1.32453i
$661$	537.182	−	930.427i	0.0316096	−	0.0547495i	−0.849788	−	0.527125i	$-0.823270\pi$
$661$	537.182	−	930.427i	0.0316096	−	0.0547495i	0.881397	+	0.472375i	$0.156603\pi$
$662$	13351.8	−	23126.0i	0.783885	−	1.35773i
$663$	−2657.23	−	4602.46i	−0.155654	−	0.269600i
$664$	−47613.0			−2.78275
$665$		0			0
$666$	−5671.84			−0.329999
$667$	−270.491	−	468.504i	−0.0157023	−	0.0271972i
$668$	−13114.1	+	22714.3i	−0.759580	+	1.31563i
$669$	1739.71	−	3013.27i	0.100540	−	0.174140i
$670$	2253.80	+	3903.69i	0.129958	+	0.225094i
$671$	797.667			0.0458921
$672$		0			0
$673$	26195.2			1.50037			0.750186	−	0.661226i	$-0.229964\pi$
$673$	26195.2			1.50037			0.750186	+	0.661226i	$0.229964\pi$
$674$	19277.7	+	33389.9i	1.10170	+	1.90821i
$675$	1881.00	−	3257.99i	0.107259	−	0.185778i
$676$	13397.3	−	23204.9i	0.762252	−	1.32026i
$677$	−2114.22	−	3661.93i	−0.120024	−	0.207887i	0.799753	−	0.600329i	$-0.204964\pi$
$677$	−2114.22	−	3661.93i	−0.120024	−	0.207887i	−0.919777	+	0.392442i	$0.871630\pi$
$678$	−46750.4			−2.64814
$679$		0			0
$680$	−13416.6			−0.756624
$681$	3878.40	+	6717.59i	0.218239	+	0.378001i
$682$	44497.3	−	77071.5i	2.49837	−	4.32730i
$683$	−13762.8	+	23837.8i	−0.771036	+	1.33547i	0.165960	+	0.986133i	$0.446928\pi$
$683$	−13762.8	+	23837.8i	−0.771036	+	1.33547i	−0.936996	+	0.349341i	$0.886405\pi$
$684$	−4542.96	−	7868.63i	−0.253954	−	0.439861i
$685$	−4614.74			−0.257402
$686$		0			0
$687$	30867.3			1.71421
$688$	3717.70	+	6439.24i	0.206012	+	0.356822i
$689$	2345.55	−	4062.60i	0.129693	−	0.224634i
$690$	−1628.36	+	2820.41i	−0.0898416	+	0.155610i
$691$	−16662.2	−	28859.8i	−0.917309	−	1.58883i	−0.803486	−	0.595324i	$-0.797024\pi$
$691$	−16662.2	−	28859.8i	−0.917309	−	1.58883i	−0.113823	−	0.993501i	$-0.536310\pi$
$692$	53021.1			2.91266
$693$		0			0
$694$	51654.8			2.82534
$695$	−490.097	−	848.872i	−0.0267488	−	0.0463303i
$696$	−3514.77	+	6087.76i	−0.191418	+	0.331546i
$697$	−211.486	+	366.305i	−0.0114930	+	0.0199065i
$698$	3469.56	+	6009.45i	0.188144	+	0.325875i
$699$	−2013.77			−0.108967
$700$		0			0
$701$	−33262.9			−1.79219			−0.896094	−	0.443864i	$-0.853607\pi$
$701$	−33262.9			−1.79219			−0.896094	+	0.443864i	$0.853607\pi$
$702$	−12488.6	−	21630.8i	−0.671439	−	1.16297i
$703$	7908.11	−	13697.2i	0.424267	−	0.734852i
$704$	40805.9	−	70677.9i	2.18456	−	3.78377i
$705$	−4210.68	−	7293.12i	−0.224941	−	0.389609i
$706$	−31392.0			−1.67345
$707$		0			0
$708$	61141.0			3.24551
$709$	−6851.52	−	11867.2i	−0.362926	−	0.628606i	0.625515	−	0.780212i	$-0.284889\pi$
$709$	−6851.52	−	11867.2i	−0.362926	−	0.628606i	−0.988441	+	0.151606i	$0.951555\pi$
$710$	12885.8	−	22318.9i	0.681122	−	1.17974i
$711$	2278.85	−	3947.08i	0.120202	−	0.208196i
$712$	−1649.79	−	2857.52i	−0.0868378	−	0.150408i
$713$	8126.14			0.426825
$714$		0			0
$715$	8009.84			0.418953
$716$	−17276.7	−	29924.0i	−0.901758	−	1.56189i
$717$	−12993.7	+	22505.7i	−0.676788	+	1.17223i
$718$	−6137.80	+	10631.0i	−0.319026	+	0.552569i
$719$	−4037.47	−	6993.10i	−0.209419	−	0.362724i	0.742113	−	0.670275i	$-0.233824\pi$
$719$	−4037.47	−	6993.10i	−0.209419	−	0.362724i	−0.951532	+	0.307551i	$0.900491\pi$
$720$	−5838.82			−0.302222
$721$		0			0
$722$	−2289.59			−0.118019
$723$	−14661.8	−	25395.0i	−0.754188	−	1.30629i
$724$	27640.5	−	47874.8i	1.41886	−	2.45753i
$725$	−261.764	+	453.389i	−0.0134092	+	0.0232254i
$726$	−17643.8	−	30559.9i	−0.901959	−	1.56224i
$727$	3668.70			0.187159			0.0935794	−	0.995612i	$-0.470169\pi$
$727$	3668.70			0.187159			0.0935794	+	0.995612i	$0.470169\pi$
$728$		0			0
$729$	21881.9			1.11172
$730$	−2009.88	−	3481.22i	−0.101903	−	0.176501i
$731$	−629.732	+	1090.73i	−0.0318625	+	0.0551875i
$732$	757.559	−	1312.13i	0.0382516	−	0.0662538i
$733$	−7490.15	−	12973.3i	−0.377428	−	0.653725i	0.613259	−	0.789882i	$-0.289858\pi$
$733$	−7490.15	−	12973.3i	−0.377428	−	0.653725i	−0.990687	+	0.136157i	$0.956525\pi$
$734$	39918.2			2.00737
$735$		0			0
$736$	15840.7			0.793338
$737$	−4350.47	−	7535.23i	−0.217438	−	0.376613i
$738$	−163.447	+	283.098i	−0.00815252	+	0.0141206i
$739$	−3265.30	+	5655.66i	−0.162538	+	0.281525i	−0.935778	−	0.352589i	$-0.885301\pi$
$739$	−3265.30	+	5655.66i	−0.162538	+	0.281525i	0.773240	+	0.634114i	$0.218635\pi$
$740$	−10504.8	−	18194.9i	−0.521846	−	0.903863i
$741$	11453.3			0.567812
$742$		0			0
$743$	25952.0			1.28141			0.640704	−	0.767788i	$-0.278643\pi$
$743$	25952.0			1.28141			0.640704	+	0.767788i	$0.278643\pi$
$744$	−52795.7	−	91444.8i	−2.60159	−	4.50609i
$745$	−1950.93	+	3379.11i	−0.0959416	+	0.166176i
$746$	−17453.1	+	30229.7i	−0.856573	+	1.48363i
$747$	−1754.93	−	3039.62i	−0.0859564	−	0.148881i
$748$	41459.6			2.02662
$749$		0			0
$750$	3151.65			0.153443
$751$	7046.97	+	12205.7i	0.342407	+	0.593066i	0.984879	−	0.173243i	$-0.0554246\pi$
$751$	7046.97	+	12205.7i	0.342407	+	0.593066i	−0.642472	+	0.766309i	$0.722091\pi$
$752$	−39741.8	+	68834.8i	−1.92717	+	3.33796i
$753$	726.285	−	1257.96i	0.0351491	−	0.0608801i
$754$	1737.93	+	3010.19i	0.0839414	+	0.145391i
$755$	−11597.1			−0.559024
$756$		0			0
$757$	−2554.41			−0.122644			−0.0613220	−	0.998118i	$-0.519532\pi$
$757$	−2554.41			−0.122644			−0.0613220	+	0.998118i	$0.519532\pi$
$758$	11498.6	+	19916.2i	0.550987	+	0.954338i
$759$	3143.20	−	5444.18i	0.150317	−	0.260357i
$760$	14457.3	−	25040.7i	0.690027	−	1.19516i
$761$	1109.54	+	1921.78i	0.0528527	+	0.0915435i	0.891241	−	0.453529i	$-0.149835\pi$
$761$	1109.54	+	1921.78i	0.0528527	+	0.0915435i	−0.838389	+	0.545073i	$0.816502\pi$
$762$	35160.1			1.67154
$763$		0			0
$764$	−38856.5			−1.84003
$765$	−494.512	−	856.520i	−0.0233714	−	0.0404805i
$766$	−18088.5	+	31330.2i	−0.853217	+	1.47781i
$767$	9442.31	−	16354.6i	0.444514	−	0.769921i
$768$	−15666.7	−	27135.6i	−0.736100	−	1.27496i
$769$	22466.2			1.05352			0.526758	−	0.850015i	$-0.323408\pi$
$769$	22466.2			1.05352			0.526758	+	0.850015i	$0.323408\pi$
$770$		0			0
$771$	36609.3			1.71006
$772$	16422.5	+	28444.6i	0.765620	+	1.32609i
$773$	4837.39	−	8378.61i	0.225083	−	0.389855i	−0.731262	−	0.682097i	$-0.761068\pi$
$773$	4837.39	−	8378.61i	0.225083	−	0.389855i	0.956344	+	0.292242i	$0.0944014\pi$
$774$	−486.687	+	842.967i	−0.0226016	+	0.0391470i
$775$	−3931.98	−	6810.39i	−0.182246	−	0.315660i
$776$	−121253.			−5.60920
$777$		0			0
$778$	−34498.2			−1.58974
$779$	−455.780	−	789.434i	−0.0209628	−	0.0363086i
$780$	7607.10	−	13175.9i	0.349203	−	0.604836i
$781$	−24873.3	+	43081.8i	−1.13961	+	1.97387i
$782$	2603.32	+	4509.08i	0.119047	+	0.206195i
$783$	−3151.23			−0.143826
$784$		0			0
$785$	−5114.51			−0.232541
$786$	22218.1	+	38482.9i	1.00826	+	1.74636i
$787$	−10471.4	+	18137.0i	−0.474288	+	0.821491i	−0.999567	−	0.0294391i	$-0.990628\pi$
$787$	−10471.4	+	18137.0i	−0.474288	+	0.821491i	0.525278	+	0.850930i	$0.323961\pi$
$788$	−7473.04	+	12943.7i	−0.337838	+	0.585152i
$789$	−12170.9	−	21080.6i	−0.549171	−	0.951192i
$790$	23219.5			1.04571
$791$		0			0
$792$	20015.1			0.897989
$793$	−233.987	−	405.278i	−0.0104781	−	0.0181486i
$794$	11499.6	−	19917.9i	0.513986	−	0.890251i
$795$	−1781.47	+	3085.60i	−0.0794746	+	0.137654i
$796$	35113.9	+	60819.1i	1.56354	+	2.70813i
$797$	−23526.6			−1.04561			−0.522807	−	0.852451i	$-0.675115\pi$
$797$	−23526.6			−1.04561			−0.522807	+	0.852451i	$0.675115\pi$
$798$		0			0
$799$	−13463.5			−0.596127
$800$	−7664.82	−	13275.9i	−0.338741	−	0.586716i
$801$	121.616	−	210.646i	0.00536468	−	0.00929189i
$802$	23913.6	−	41419.5i	1.05289	−	1.82366i
$803$	3879.65	+	6719.74i	0.170498	+	0.295311i
$804$	−16526.9			−0.724948
$805$		0			0
$806$	−52211.3			−2.28172
$807$	2984.36	+	5169.07i	0.130179	+	0.225477i
$808$	−15648.1	+	27103.3i	−0.681308	+	1.18006i
$809$	9101.12	−	15763.6i	0.395523	−	0.685067i	−0.597644	−	0.801761i	$-0.703897\pi$
$809$	9101.12	−	15763.6i	0.395523	−	0.685067i	0.993168	+	0.116695i	$0.0372299\pi$
$810$	7543.28	+	13065.3i	0.327214	+	0.566752i
$811$	2510.24			0.108689			0.0543443	−	0.998522i	$-0.482693\pi$
$811$	2510.24			0.108689			0.0543443	+	0.998522i	$0.482693\pi$
$812$		0			0
$813$	−21906.5			−0.945012
$814$	27888.3	+	48304.0i	1.20084	+	2.07992i
$815$	3376.56	−	5848.38i	0.145124	−	0.251362i
$816$	19048.4	−	32992.9i	0.817192	−	1.41542i
$817$	−1357.15	−	2350.66i	−0.0581160	−	0.100660i
$818$	1728.24			0.0738711
$819$		0			0
$820$	−1210.88			−0.0515681
$821$	−8949.81	−	15501.5i	−0.380451	−	0.658961i	0.610675	−	0.791881i	$-0.290898\pi$
$821$	−8949.81	−	15501.5i	−0.380451	−	0.658961i	−0.991127	+	0.132920i	$0.957565\pi$
$822$	11635.2	−	20152.8i	0.493705	−	0.855123i
$823$	−7019.75	+	12158.6i	−0.297318	+	0.514970i	−0.975522	−	0.219904i	$-0.929426\pi$
$823$	−7019.75	+	12158.6i	−0.297318	+	0.514970i	0.678203	+	0.734874i	$0.262759\pi$
$824$	12455.2	+	21573.0i	0.526573	+	0.912051i
$825$	−6083.58			−0.256731
$826$		0			0
$827$	15127.4			0.636073			0.318036	−	0.948079i	$-0.396977\pi$
$827$	15127.4			0.636073			0.318036	+	0.948079i	$0.396977\pi$
$828$	1462.88	+	2533.79i	0.0613994	+	0.106347i
$829$	10993.2	−	19040.8i	0.460568	−	0.797727i	−0.538421	−	0.842676i	$-0.680979\pi$
$829$	10993.2	−	19040.8i	0.460568	−	0.797727i	0.998989	+	0.0449487i	$0.0143124\pi$
$830$	8940.60	−	15485.6i	0.373895	−	0.647605i
$831$	−20859.4	−	36129.5i	−0.870762	−	1.50820i
$832$	−47880.0			−1.99512
$833$		0			0
$834$	4942.76			0.205220
$835$	−3076.44	−	5328.56i	−0.127503	−	0.220841i
$836$	−44675.3	+	77379.9i	−1.84824	+	3.20124i
$837$	23667.4	−	40993.2i	0.977378	−	1.69287i
$838$	−34621.7	−	59966.6i	−1.42719	−	2.47197i
$839$	2276.89			0.0936914			0.0468457	−	0.998902i	$-0.485083\pi$
$839$	2276.89			0.0936914			0.0468457	+	0.998902i	$0.485083\pi$
$840$		0			0
$841$	−23950.5			−0.982019
$842$	18265.9	+	31637.5i	0.747607	+	1.29489i
$843$	863.623	−	1495.84i	0.0352844	−	0.0611144i
$844$	−43505.1	+	75353.0i	−1.77430	+	3.07317i
$845$	3142.89	+	5443.65i	0.127951	+	0.221618i
$846$	−10405.3			−0.422861
$847$		0			0
$848$	33628.2			1.36179
$849$	−13556.7	−	23480.9i	−0.548015	−	0.949190i
$850$	2519.33	−	4363.60i	0.101661	−	0.176083i
$851$	−2546.50	+	4410.67i	−0.102577	+	0.177668i
$852$	47245.3	+	81831.3i	1.89976	+	3.29048i
$853$	−13342.6			−0.535570			−0.267785	−	0.963479i	$-0.586292\pi$
$853$	−13342.6			−0.535570			−0.267785	+	0.963479i	$0.586292\pi$
$854$		0			0
$855$	2131.47			0.0852571
$856$	−7825.31	−	13553.8i	−0.312457	−	0.541192i
$857$	9345.43	−	16186.8i	0.372502	−	0.645192i	−0.617448	−	0.786612i	$-0.711833\pi$
$857$	9345.43	−	16186.8i	0.372502	−	0.645192i	0.989950	+	0.141420i	$0.0451668\pi$
$858$	−20195.4	+	34979.4i	−0.803565	+	1.39182i
$859$	9159.45	+	15864.6i	0.363814	+	0.630144i	0.988585	−	0.150664i	$-0.0481410\pi$
$859$	9159.45	+	15864.6i	0.363814	+	0.630144i	−0.624771	+	0.780808i	$0.714808\pi$
$860$	−3605.58			−0.142964
$861$		0			0
$862$	−28071.3			−1.10918
$863$	−19066.6	−	33024.3i	−0.752067	−	1.30262i	−0.946819	−	0.321765i	$-0.895724\pi$
$863$	−19066.6	−	33024.3i	−0.752067	−	1.30262i	0.194753	−	0.980852i	$-0.437610\pi$
$864$	46136.2	−	79910.2i	1.81665	−	3.14653i
$865$	−6219.13	+	10771.9i	−0.244459	+	0.423415i
$866$	−11483.6	−	19890.2i	−0.450612	−	0.780482i
$867$	−16426.0			−0.643432
$868$		0			0
$869$	−44820.3			−1.74962
$870$	−1319.98	−	2286.28i	−0.0514386	−	0.0890943i
$871$	−2552.33	+	4420.77i	−0.0992910	+	0.171977i
$872$	−62510.9	+	108272.i	−2.42762	+	4.20477i
$873$	−4469.17	−	7740.82i	−0.173263	−	0.300100i
$874$	−11221.0			−0.434273
$875$		0			0
$876$	14738.3			0.568449
$877$	9853.73	+	17067.2i	0.379404	+	0.657146i	0.990976	−	0.134042i	$-0.0427959\pi$
$877$	9853.73	+	17067.2i	0.379404	+	0.657146i	−0.611572	+	0.791189i	$0.709463\pi$
$878$	−14710.7	+	25479.7i	−0.565448	+	0.979385i
$879$	17332.3	−	30020.5i	0.665079	−	1.15195i
$880$	28709.4	+	49726.1i	1.09977	+	1.90485i
$881$	14091.5			0.538883			0.269441	−	0.963017i	$-0.413161\pi$
$881$	14091.5			0.538883			0.269441	+	0.963017i	$0.413161\pi$
$882$		0			0
$883$	3115.87			0.118751			0.0593757	−	0.998236i	$-0.481089\pi$
$883$	3115.87			0.118751			0.0593757	+	0.998236i	$0.481089\pi$
$884$	−12161.7	−	21064.8i	−0.462719	−	0.801453i
$885$	−7171.56	+	12421.5i	−0.272395	+	0.471801i
$886$	31114.9	−	53892.6i	1.17983	−	2.04352i
$887$	19367.3	+	33545.1i	0.733134	+	1.26983i	0.955537	+	0.294871i	$0.0952768\pi$
$887$	19367.3	+	33545.1i	0.733134	+	1.26983i	−0.222403	+	0.974955i	$0.571390\pi$
$888$	66178.6			2.50091
$889$		0			0
$890$	1239.17			0.0466708
$891$	−14560.7	−	25219.8i	−0.547475	−	0.948255i
$892$	7962.39	−	13791.3i	0.298879	−	0.517674i
$893$	14507.8	−	25128.3i	0.543657	−	0.941641i
$894$	−9837.84	−	17039.6i	−0.368039	−	0.637461i
$895$	8105.89			0.302737
$896$		0			0
$897$	−3688.10			−0.137282
$898$	45612.9	+	79003.9i	1.69501	+	2.93585i
$899$	−3293.60	+	5704.69i	−0.122189	+	0.211637i
$900$	1415.69	−	2452.04i	0.0524328	−	0.0908163i
$901$	2848.10	+	4933.06i	0.105310	+	0.182402i
$902$	3214.66			0.118666
$903$		0			0
$904$	−133657.			−4.91744
$905$	6484.21	+	11231.0i	0.238169	+	0.412520i
$906$	29240.1	−	50645.4i	1.07223	−	1.85715i
$907$	−9621.43	+	16664.8i	−0.352232	+	0.610083i	−0.986640	−	0.162915i	$-0.947910\pi$
$907$	−9621.43	+	16664.8i	−0.352232	+	0.610083i	0.634408	+	0.772998i	$0.281244\pi$
$908$	17750.8	+	30745.4i	0.648769	+	1.12370i
$909$	−2307.03			−0.0841799
$910$		0			0
$911$	34613.3			1.25882			0.629412	−	0.777072i	$-0.283296\pi$
$911$	34613.3			1.25882			0.629412	+	0.777072i	$0.283296\pi$
$912$	41051.8	+	71103.8i	1.49053	+	2.58167i
$913$	−17257.9	+	29891.5i	−0.625578	+	1.08353i
$914$	−41550.0	+	71966.8i	−1.50367	+	2.60443i
$915$	177.716	+	307.814i	0.00642090	+	0.0111213i
$916$	141275.			5.09591
$917$		0			0
$918$	30328.7			1.09041
$919$	−12913.2	−	22366.3i	−0.463511	−	0.802825i	0.535622	−	0.844458i	$-0.320077\pi$
$919$	−12913.2	−	22366.3i	−0.463511	−	0.802825i	−0.999133	+	0.0416333i	$0.986744\pi$
$920$	−4655.40	+	8063.40i	−0.166831	+	0.288959i
$921$	−1773.50	+	3071.80i	−0.0634516	+	0.109901i
$922$	38003.5	+	65824.0i	1.35746	+	2.35119i
$923$	29185.3			1.04079
$924$		0			0
$925$	4928.68			0.175194
$926$	23446.9	+	40611.2i	0.832087	+	1.44122i
$927$	−918.147	+	1590.28i	−0.0325307	+	0.0563448i
$928$	−6420.40	+	11120.5i	−0.227112	+	0.393370i
$929$	9725.79	+	16845.6i	0.343480	+	0.594925i	0.985076	−	0.172118i	$-0.0550609\pi$
$929$	9725.79	+	16845.6i	0.343480	+	0.594925i	−0.641596	+	0.767042i	$0.721728\pi$
$930$	39655.1			1.39822
$931$		0			0
$932$	−9216.70			−0.323930
$933$	17972.4	+	31129.1i	0.630643	+	1.09231i
$934$	18989.6	−	32890.9i	0.665265	−	1.15227i
$935$	−4863.02	+	8422.99i	−0.170094	+	0.294611i
$936$	−5871.24	−	10169.3i	−0.205029	−	0.355121i
$937$	−34469.1			−1.20177			−0.600884	−	0.799336i	$-0.705185\pi$
$937$	−34469.1			−1.20177			−0.600884	+	0.799336i	$0.705185\pi$
$938$		0			0
$939$	−39844.1			−1.38473
$940$	−19271.7	−	33379.5i	−0.668694	−	1.15821i
$941$	7078.18	−	12259.8i	0.245209	−	0.424715i	−0.716981	−	0.697093i	$-0.754477\pi$
$941$	7078.18	−	12259.8i	0.245209	−	0.424715i	0.962190	+	0.272378i	$0.0878100\pi$
$942$	12895.3	−	22335.3i	0.446021	−	0.772531i
$943$	146.766	+	254.207i	0.00506826	+	0.00877848i
$944$	135375.			4.66746
$945$		0			0
$946$	9572.13			0.328982
$947$	19046.2	+	32989.0i	0.653557	+	1.13199i	0.982253	+	0.187558i	$0.0600574\pi$
$947$	19046.2	+	32989.0i	0.653557	+	1.13199i	−0.328696	+	0.944436i	$0.606609\pi$
$948$	−42566.7	+	73727.6i	−1.45833	+	2.52591i
$949$	2276.11	−	3942.34i	0.0778563	−	0.134851i
$950$	5429.47	+	9404.11i	0.185427	+	0.321168i
$951$	−36234.8			−1.23553
$952$		0			0
$953$	5037.40			0.171225			0.0856126	−	0.996329i	$-0.472715\pi$
$953$	5037.40			0.171225			0.0856126	+	0.996329i	$0.472715\pi$
$954$	2201.15	+	3812.50i	0.0747011	+	0.129386i
$955$	4557.69	−	7894.16i	0.154433	−	0.267486i
$956$	−59470.0	+	103005.i	−2.01192	+	3.48475i
$957$	2547.94	+	4413.16i	0.0860639	+	0.149067i
$958$	−98185.1			−3.31129
$959$		0			0
$960$	36365.4			1.22259
$961$	−34578.0	−	59890.9i	−1.16069	−	2.01037i
$962$	16361.5	−	28339.0i	0.548354	−	0.949777i
$963$	576.853	−	999.138i	0.0193030	−	0.0334338i
$964$	−67104.8	−	116229.i	−2.24201	−	3.88328i
$965$	−7705.14			−0.257033
$966$		0			0
$967$	11495.3			0.382278			0.191139	−	0.981563i	$-0.438782\pi$
$967$	11495.3			0.382278			0.191139	+	0.981563i	$0.438782\pi$
$968$	−50442.7	−	87369.3i	−1.67489	−	2.90099i
$969$	−6953.67	+	12044.1i	−0.230530	+	0.399290i
$970$	22768.5	−	39436.2i	0.753662	−	1.30538i
$971$	11176.4	+	19358.0i	0.369379	+	0.639783i	0.989469	−	0.144748i	$-0.0462372\pi$
$971$	11176.4	+	19358.0i	0.369379	+	0.639783i	−0.620090	+	0.784531i	$0.712904\pi$
$972$	31282.7			1.03230
$973$		0			0
$974$	89539.4			2.94561
$975$	1784.56	+	3090.94i	0.0586170	+	0.101528i
$976$	1677.35	−	2905.25i	0.0550108	−	0.0952815i
$977$	−7172.86	+	12423.8i	−0.234882	+	0.406828i	−0.959238	−	0.282598i	$-0.908804\pi$
$977$	−7172.86	+	12423.8i	−0.234882	+	0.406828i	0.724356	+	0.689426i	$0.242137\pi$
$978$	17026.8	+	29491.3i	0.556705	+	0.964241i
$979$	−2391.94			−0.0780867
$980$		0			0
$981$	−9216.15			−0.299948
$982$	−597.210	−	1034.40i	−0.0194071	−	0.0336140i
$983$	17230.4	−	29844.0i	0.559070	−	0.968338i	−0.438504	−	0.898729i	$-0.644492\pi$
$983$	17230.4	−	29844.0i	0.559070	−	0.968338i	0.997574	−	0.0696087i	$-0.0221751\pi$
$984$	1907.09	−	3303.17i	0.0617842	−	0.107013i
$985$	−1753.11	−	3036.47i	−0.0567093	−	0.0982234i
$986$	−4220.61			−0.136320
$987$		0			0
$988$	52420.2			1.68796
$989$	437.018	+	756.938i	0.0140509	+	0.0243369i
$990$	−3758.37	+	6509.69i	−0.120655	+	0.208981i
$991$	17594.8	−	30475.1i	0.563993	−	0.976864i	−0.433150	−	0.901322i	$-0.642598\pi$
$991$	17594.8	−	30475.1i	0.563993	−	0.976864i	0.997143	−	0.0755420i	$-0.0240687\pi$
$992$	−96441.4	−	167041.i	−3.08671	−	5.34634i
$993$	−22968.2			−0.734011
$994$		0			0
$995$	−16474.8			−0.524911
$996$	32780.3	+	56777.2i	1.04286	+	1.80628i
$997$	−25365.0	+	43933.4i	−0.805734	+	1.39557i	0.110060	+	0.993925i	$0.464896\pi$
$997$	−25365.0	+	43933.4i	−0.805734	+	1.39557i	−0.915794	+	0.401648i	$0.868438\pi$
$998$	−16077.6	+	27847.2i	−0.509948	+	0.883255i
$999$	14833.4	+	25692.2i	0.469777	+	0.813678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.i.116.1		4
7.2	even	3	inner	245.4.e.i.226.1		4
7.3	odd	6		35.4.a.b.1.2	✓	2
7.4	even	3		245.4.a.k.1.2		2
7.5	odd	6		245.4.e.h.226.1		4
7.6	odd	2		245.4.e.h.116.1		4
21.11	odd	6		2205.4.a.u.1.1		2
21.17	even	6		315.4.a.f.1.1		2
28.3	even	6		560.4.a.r.1.2		2
35.3	even	12		175.4.b.c.99.1		4
35.4	even	6		1225.4.a.m.1.1		2
35.17	even	12		175.4.b.c.99.4		4
35.24	odd	6		175.4.a.c.1.1		2
56.3	even	6		2240.4.a.bo.1.1		2
56.45	odd	6		2240.4.a.bn.1.2		2
105.59	even	6		1575.4.a.z.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.b.1.2	✓	2	7.3	odd	6
175.4.a.c.1.1		2	35.24	odd	6
175.4.b.c.99.1		4	35.3	even	12
175.4.b.c.99.4		4	35.17	even	12
245.4.a.k.1.2		2	7.4	even	3
245.4.e.h.116.1		4	7.6	odd	2
245.4.e.h.226.1		4	7.5	odd	6
245.4.e.i.116.1		4	1.1	even	1	trivial
245.4.e.i.226.1		4	7.2	even	3	inner
315.4.a.f.1.1		2	21.17	even	6
560.4.a.r.1.2		2	28.3	even	6
1225.4.a.m.1.1		2	35.4	even	6
1575.4.a.z.1.2		2	105.59	even	6
2205.4.a.u.1.1		2	21.11	odd	6
2240.4.a.bn.1.2		2	56.45	odd	6
2240.4.a.bo.1.1		2	56.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.70711 - 4.68885i) q^{2} +(-2.32843 + 4.03295i) q^{3} +(-10.6569 + 18.4582i) q^{4} +(-2.50000 - 4.33013i) q^{5} +25.2132 q^{6} +72.0833 q^{8} +(2.65685 + 4.60181i) q^{9} +O(q^{10})\)	\(q+(-2.70711 - 4.68885i) q^{2} +(-2.32843 + 4.03295i) q^{3} +(-10.6569 + 18.4582i) q^{4} +(-2.50000 - 4.33013i) q^{5} +25.2132 q^{6} +72.0833 q^{8} +(2.65685 + 4.60181i) q^{9} +(-13.5355 + 23.4442i) q^{10} +(26.1274 - 45.2540i) q^{11} +(-49.6274 - 85.9572i) q^{12} -30.6569 q^{13} +23.2843 q^{15} +(-109.882 - 190.322i) q^{16} +(18.6127 - 32.2381i) q^{17} +(14.3848 - 24.9152i) q^{18} +(40.1127 + 69.4772i) q^{19} +106.569 q^{20} -282.919 q^{22} +(-12.9167 - 22.3724i) q^{23} +(-167.841 + 290.708i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(82.9914 + 143.745i) q^{26} -150.480 q^{27} +20.9411 q^{29} +(-63.0330 - 109.176i) q^{30} +(-157.279 + 272.416i) q^{31} +(-306.593 + 531.035i) q^{32} +(121.672 + 210.741i) q^{33} -201.546 q^{34} -113.255 q^{36} +(-98.5736 - 170.734i) q^{37} +(217.179 - 376.165i) q^{38} +(71.3823 - 123.638i) q^{39} +(-180.208 - 312.130i) q^{40} -11.3625 q^{41} -33.8335 q^{43} +(556.872 + 964.531i) q^{44} +(13.2843 - 23.0090i) q^{45} +(-69.9340 + 121.129i) q^{46} +(-180.838 - 313.221i) q^{47} +1023.41 q^{48} +135.355 q^{50} +(86.6766 + 150.128i) q^{51} +(326.706 - 565.871i) q^{52} +(-76.5097 + 132.519i) q^{53} +(407.366 + 705.579i) q^{54} -261.274 q^{55} -373.598 q^{57} +(-56.6899 - 98.1897i) q^{58} +(-308.000 + 533.472i) q^{59} +(-248.137 + 429.786i) q^{60} +(7.63247 + 13.2198i) q^{61} +1703.09 q^{62} +1561.80 q^{64} +(76.6421 + 132.748i) q^{65} +(658.756 - 1141.00i) q^{66} +(83.2548 - 144.202i) q^{67} +(396.706 + 687.114i) q^{68} +120.303 q^{69} -952.000 q^{71} +(191.515 + 331.713i) q^{72} +(-74.2447 + 128.596i) q^{73} +(-533.698 + 924.393i) q^{74} +(-58.2107 - 100.824i) q^{75} -1709.90 q^{76} -772.958 q^{78} +(-428.862 - 742.812i) q^{79} +(-549.411 + 951.608i) q^{80} +(278.647 - 482.631i) q^{81} +(30.7595 + 53.2769i) q^{82} -660.528 q^{83} -186.127 q^{85} +(91.5908 + 158.640i) q^{86} +(-48.7599 + 84.4546i) q^{87} +(1883.35 - 3262.06i) q^{88} +(-22.8873 - 39.6420i) q^{89} -143.848 q^{90} +550.607 q^{92} +(-732.426 - 1268.60i) q^{93} +(-979.096 + 1695.84i) q^{94} +(200.563 - 347.386i) q^{95} +(-1427.76 - 2472.95i) q^{96} -1682.13 q^{97} +277.667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 2 q^{3} - 20 q^{4} - 10 q^{5} + 16 q^{6} + 96 q^{8} - 12 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 + 2 * q^3 - 20 * q^4 - 10 * q^5 + 16 * q^6 + 96 * q^8 - 12 * q^9	\( 4 q - 8 q^{2} + 2 q^{3} - 20 q^{4} - 10 q^{5} + 16 q^{6} + 96 q^{8} - 12 q^{9} - 40 q^{10} + 14 q^{11} - 108 q^{12} - 100 q^{13} - 20 q^{15} - 168 q^{16} - 50 q^{17} - 16 q^{18} + 36 q^{19} + 200 q^{20} - 368 q^{22} - 244 q^{23} - 496 q^{24} - 50 q^{25} + 216 q^{26} - 172 q^{27} - 52 q^{29} - 40 q^{30} - 120 q^{31} - 672 q^{32} + 498 q^{33} + 48 q^{34} - 272 q^{36} - 564 q^{37} + 320 q^{38} + 14 q^{39} - 240 q^{40} + 656 q^{41} - 520 q^{43} + 1164 q^{44} - 60 q^{45} - 704 q^{46} - 350 q^{47} + 2736 q^{48} + 400 q^{50} + 754 q^{51} + 628 q^{52} + 56 q^{53} + 648 q^{54} - 140 q^{55} - 1336 q^{57} + 8 q^{58} - 1232 q^{59} - 540 q^{60} + 336 q^{61} + 2400 q^{62} + 4256 q^{64} + 250 q^{65} + 1976 q^{66} + 152 q^{67} + 908 q^{68} - 2664 q^{69} - 3808 q^{71} + 800 q^{72} + 676 q^{73} - 2016 q^{74} + 50 q^{75} - 3536 q^{76} - 880 q^{78} - 1014 q^{79} - 840 q^{80} + 1454 q^{81} - 816 q^{82} + 752 q^{83} + 500 q^{85} + 768 q^{86} - 410 q^{87} + 4688 q^{88} - 216 q^{89} + 160 q^{90} + 528 q^{92} - 2760 q^{93} - 1928 q^{94} + 180 q^{95} - 2464 q^{96} - 5484 q^{97} + 1880 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 2 * q^3 - 20 * q^4 - 10 * q^5 + 16 * q^6 + 96 * q^8 - 12 * q^9 - 40 * q^10 + 14 * q^11 - 108 * q^12 - 100 * q^13 - 20 * q^15 - 168 * q^16 - 50 * q^17 - 16 * q^18 + 36 * q^19 + 200 * q^20 - 368 * q^22 - 244 * q^23 - 496 * q^24 - 50 * q^25 + 216 * q^26 - 172 * q^27 - 52 * q^29 - 40 * q^30 - 120 * q^31 - 672 * q^32 + 498 * q^33 + 48 * q^34 - 272 * q^36 - 564 * q^37 + 320 * q^38 + 14 * q^39 - 240 * q^40 + 656 * q^41 - 520 * q^43 + 1164 * q^44 - 60 * q^45 - 704 * q^46 - 350 * q^47 + 2736 * q^48 + 400 * q^50 + 754 * q^51 + 628 * q^52 + 56 * q^53 + 648 * q^54 - 140 * q^55 - 1336 * q^57 + 8 * q^58 - 1232 * q^59 - 540 * q^60 + 336 * q^61 + 2400 * q^62 + 4256 * q^64 + 250 * q^65 + 1976 * q^66 + 152 * q^67 + 908 * q^68 - 2664 * q^69 - 3808 * q^71 + 800 * q^72 + 676 * q^73 - 2016 * q^74 + 50 * q^75 - 3536 * q^76 - 880 * q^78 - 1014 * q^79 - 840 * q^80 + 1454 * q^81 - 816 * q^82 + 752 * q^83 + 500 * q^85 + 768 * q^86 - 410 * q^87 + 4688 * q^88 - 216 * q^89 + 160 * q^90 + 528 * q^92 - 2760 * q^93 - 1928 * q^94 + 180 * q^95 - 2464 * q^96 - 5484 * q^97 + 1880 * q^99

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